基于拟法锥条件的非凸非线性规划问题的同伦内点法

1 引言 考虑如下的非线性规划问题: min f(x) (1) 8.t.gi(x)≤0,i=1,…,m,其中xR~n,我们总假定f,gi是二次连续可微的。 称Ω={xR~n|gi(x)≤0,i=1,…,m}为(1)的行域;Ω~0={xR~n|gi(x)<0,i=1,…,m}为(1)的严格可行域;Ω=Ω\Ω~0为Ω的边界。 此外,记     

Globally Convergent Interior Point Methods for Variational Inequalities in Unbounded Sets

The finite-dimensional variational inequality problem (VIP) has been studied extensively in the literature because of its successful applications in many fields such as economics, transportation, regional science and operations research. Barker and Pang[1] have given an excellent survey of theories, methods and applications of VIPs.     

The Eigenvalue Method for Computing High-dimensional Varieties

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Interpolation on Algebraic Manifold

In traditional researches of multivariate interpolation,people always assume that inter—polation nodes are not on any algebraic manifold of low degree;more precisely,there existsno polynomial with low degree vanishing at the nodes[1】.In this case,the interpolationnodes are said to be on‘‘General Position”.But in this paper,we are to discuss interpolationon algebraic manifold,that is,the interpolation nodes are just on some algebraic manifolds.Definition 1三e￡S be an irreducible algebrai…     

An Interior Point Path-following Method for Nonconvex Programming With Quasi Normal Cone Condition

Since Karmarkar's famous paper[1] on a new polynomial interior point algorithm for linearprogramming was published in 1984, interior point methods have been proven to be a class ofefficient methods for mathematical programming and have been paid much attention. UP tillnow) theories, algorithms and applications of interior point methods for linear programming aswell as convex nonlinear programming have been well studied (see [2] and references therein),however, few results on nonconvex programm…     

The Aggregate Homotopy Method for Constrained Sequential Max-min Problems

Consider the Constrained Sequentialm二一min problem(CSMMP):梁bnn{蚕(x)S·t.垂(x)=二二1〕laX】刀In 1三坛三ml三J三认{人j(x)}}(l)1lla火11〕In1三坛三天1三J三p‘{夕‘,(x)}三。,which has many applieations in engineering design and deeision making(see【11 and thereferenees therein).This 15 a typieal elass of nondifferential optimization problems and,ingeneral,it 15 noneonvex even if all九5 and夕坛j are eonvex funetions even linear funetions,andhenee,it 15 diffieult in theoretieal researeh as well…     

在环面同态作用下零维理想的性质

本文以矩阵变换和整理论为工具，研究了在环面同态作用下零维理想的性质，证明了零维理想的环面同态矩阵是满秩的，并且刻画了零维理想在环面作用下的对应关系．     

2-齐次多项式集合的吴消元法

1引言 考虑2-齐次多项式集合p,两组变量分别记为x=(x_1…,x_n)与y=(y_1…,y_m),p的零点集Zero(P)为有限点集.利用吴消无法([7],[6])可以将此类多项式集合完全三角化从而求得全部解,但这样消元的复杂度甚高.